On the orientational analysis of planar fibre systems from digital images.

The orientational characteristics of fibres in digital images are studied. The fibres are modelled by a planar Boolean model whose typical grain is a thick (coloured) fibre. The aim is to make stereological inference on the rose of directions of the unobservable central fibres from observations made on a digital image of the thick fibres. For central fibres, the relation between the rose of directions and the point intensity, observed on a sampling line, is known. We derive, under regularity conditions, the relation between the unobservable point intensity and the scaled variogram observed on the line in a binary and a greyscale image. Using such a relation, it is possible to draw inference about the rose of directions from the scaled variogram, which is easy and quick to determine in a digital image.